Because birthdays aren't that personal. Let's do some math- There are 365 days, that means 365 potential birthdays. The world population, according to google, is 7,874,965,825. That's almost 8 billion people. 365/7,874,965,825 = 21,574,509. This means you're estimated to share your birthday with about 21 million other people, that's twice the population of the Czech Rupublic.
So, in conclusion? I highly, highly, HIGHLY doubt someone would be able to identify you through your birthday alone.